KöMaL 2016 B4778

Let $D$ denote an interior point of an acute-angled triangle $ABC$ . Construct the circles of diameters $AD$ , $BD$ and $CD$ , and draw a tangent from each of the points $A$ , $B$ and $C$ to each of the two circles not passing through it. Prove that the sum of the squares of the six tangents equals the sum of the squares of the sides of the triangle.